Question

The function $f \left(x\right)=2x^{3}-15x^{2} +36x +6$ is strictly decreasing in the interval

• A. (2, 3)
• B. $\left(-\infty, 2\right)$
• C. (3, 4)
• D. $\left(-\infty, 3\right)\cup\left(4, \infty\right)$
• E. $\left(-\infty, 2\right)\cup\left(3, \infty\right)$

Answer 1

Answer: (A)

Given, $f(x)=2 x^{3}-15 x^{2}+36 x+6$
On differentiating both sides w.r.t. $x$, we get
$f^{'}(x)=6 x^{2}-30 x+36$
For strictly decreasing,
$f^{'}(x)<0$
$\Rightarrow 6\left(x^{2}-5 x+6\right)<0$
$\Rightarrow (x-3)(x-2)<0$
$\Rightarrow 2 < x < 3$
$\therefore x \in(2,3)$